Epoch AI: 14 Problems That No One Has Solved (Yet)

Remember those glorious days when we used to joke about neural networks that couldn't add two three-digit numbers without hallucinating? Those days are officially over. We've rapidly transitioned from the era of "look how funny the robot writes poetry" to the era of "look how the algorithm tries to break the foundation of the universe."

Back in mid-2024, GPT-4 was stumbling on high school-level problems, but by the end of 2025, new models began cracking olympiad problems like nuts. Yet olympiads are still problems with known answers. Researchers from Epoch AI decided it was time to stop giving neural networks cheat sheets and launched FrontierMath.

This is a list of 14 problems that no one on the planet has solved.

The essence of the FrontierMath project is to test AI's ability to generate fundamentally new knowledge. These aren't textbook exercises that can be found in training datasets. Each of these fourteen problems was formulated by an active research scientist, each was attempted by at least two high-level professionals, and each is worthy of publication in a leading scientific journal. There are no hints on the internet and no off-the-shelf algorithms. These are "white spots" on the map of modern mathematics that have been ignored for decades or simply couldn't be overcome by human minds.

Let's delve into the details to understand the scale of the challenge. One of the problems concerns the Mathieu group M23. Mathematicians love symmetries, but sporadic groups are such "mathematical monsters" that don't fit into any general series.

For most of them, scientists have already found polynomials with corresponding Galois groups, but M23 remains the last stronghold, a gap in research that has been ongoing for many years. Finding this polynomial would close an entire chapter in algebra. Another problem seems simpler only at first glance: you need to devise an algorithm that determines whether a knot can be untied in a single move.

Topologists call this "unknotting number equals one." This is a fundamental question in low-dimensional topology that still has no clear answer.

Why is this important right now? The AI industry has reached a point where simply increasing the amount of data no longer produces explosive growth in quality. We've trained models to imitate human speech and compile existing knowledge, but we're still waiting for the moment when a neural network makes a scientific discovery. If a model solves even one of these problems, it won't simply be a "technological achievement." It will become a full-fledged scientific result that goes into a peer-reviewed journal not because of AI hype, but because of the value of the solution itself. We're talking about transforming AI from an advanced search engine into a full-fledged research colleague.

The connection to previous events is clearly traceable here. After models began massively winning tests like MATH or GSM8K, it became clear that we need new measurement tools. FrontierMath is an attempt to feel out the boundary where memory ends and intelligence begins. This is a challenge not only for OpenAI or Anthropic, but for the entire scaling concept. Now it's not enough to have the biggest GPU cluster; you need an algorithm capable of deep logical reasoning under conditions of complete uncertainty. This is a stress test for all promises about "strong AI" or AGI.

What does this mean for us? We're on the threshold of a situation where AI could become the key to solving problems in materials science, cryptography, or quantum physics through mathematics. If a neural network succeeds with knot topology or Mathieu groups, it will be able to design new molecules or optimize supply chains at a level inaccessible to humans. This would mean we've finally obtained a tool that's smarter than us in the most complex abstract fields. And the irony here is that we might not immediately understand exactly how the AI arrived at the solution, but the result will change our physical reality.

The key point: FrontierMath is the final boss for the current generation of neural networks. Will something like GPT-5 or Claude 4 be able to take this barrier, or will we have to wait for fundamentally new architectures?